Details

analyze1.2s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample193.0ms

Algorithm

intervals

Results

59.0ms	105×	body	1280	valid
25.0ms	22×	body	1280	nan
24.0ms	57×	body	640	valid
22.0ms	31×	body	640	nan
16.0ms	92×	body	80	overflowed
8.0ms	25×	body	320	valid
6.0ms	10×	body	640	invalid
5.0ms	12×	body	320	nan
5.0ms	55×	body	80	valid
3.0ms	9×	body	320	invalid
3.0ms	14×	body	160	valid
2.0ms	7×	body	160	nan
1.0ms	22×	body	80	nan
1.0ms	1×	body	1280	invalid
1.0ms	7×	body	80	invalid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4912	13
1	4912	13

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.8b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
26×	`pow-unpow_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
17×	`unpow-prod-down_binary64`
9×	`difference-of-squares_binary64`
8×	`sqr-pow_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series56.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
10.0ms	(pow.f64 x (/.f64 1 n))
33.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify82.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4922	1073
1	4922	1073

prune125.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Merged error: 19.7b

Counts

88 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
2.6b	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
2.7b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
27×	`unpow-prod-down_binary64`
26×	`pow-unpow_binary64`
22×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64` `times-frac_binary64`
16×	`log-pow_binary64`
15×	`exp-prod_binary64`
14×	`sqr-pow_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
4×	`log-prod_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64`
2×	`pow-to-exp_binary64` `sub-neg_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 107

Calls

4 calls:

6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))
11.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
15.0ms	(pow.f64 x (/.f64 1 n))
29.0ms	(log.f64 (exp.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))))
31.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

simplify81.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4973	1533
1	4973	1533

prune144.0ms

Filtered

89 candidates to 119 candidates (-33.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Merged error: 19.7b

Counts

125 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
0.3b	(cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3))
2.7b	(-.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)) (pow.f64 x (/.f64 1 n)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
47×	`unpow-prod-down_binary64`
46×	`cbrt-prod_binary64`
33×	`*-un-lft-identity_binary64`
27×	`difference-of-squares_binary64`
26×	`pow-unpow_binary64`
25×	`add-cube-cbrt_binary64`
23×	`sqr-pow_binary64`
18×	`times-frac_binary64`
17×	`cube-prod_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64`
2×	`pow-to-exp_binary64` `pow-pow_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `diff-log_binary64` `pow1/3_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 125

Calls

4 calls:

6.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1 n))
9.0ms	(cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3))
17.0ms	(-.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)) (pow.f64 x (/.f64 1 n)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
10.0ms	(pow.f64 x (/.f64 1 n))
13.0ms	(cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3))
29.0ms	(-.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) 3)) (pow.f64 x (/.f64 1 n)))

simplify54.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4984	1981
1	4984	1981

prune140.0ms

Filtered

87 candidates to 137 candidates (-57.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	136	8	144

Merged error: 19.7b

Counts

144 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1/2 n))
0.0b	(pow.f64 x (/.f64 1/2 n))
2.9b	(-.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)) (pow.f64 x (/.f64 1/2 n)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
39×	`pow-unpow_binary64`
33×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
27×	`times-frac_binary64`
23×	`unpow-prod-down_binary64`
12×	`difference-of-squares_binary64`
10×	`sqr-pow_binary64`
8×	`pow1_binary64`
7×	`add-exp-log_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64`
5×	`pow-pow_binary64`
4×	`add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 112

Calls

4 calls:

6.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n))
4.0ms	(pow.f64 x (/.f64 1/2 n))
4.0ms	(pow.f64 x (/.f64 1/2 n))
13.0ms	(-.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)) (pow.f64 x (/.f64 1/2 n)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n))
12.0ms	(pow.f64 x (/.f64 1/2 n))
11.0ms	(pow.f64 x (/.f64 1/2 n))
39.0ms	(-.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 1 n)) (pow.f64 x (/.f64 1/2 n)))

simplify63.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4973	1647
1	4973	1647

prune179.0ms

Filtered

92 candidates to 124 candidates (-34.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	123	9	132

Merged error: 19.7b

Counts

132 → 9

regimes296.0ms

Accuracy

84.1% (1.7b remaining)

Error of 24.1b against oracle of 22.4b and baseline of 33.2b

bsearch2.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	81
1	77	81

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.1s	3699×	body	1280	valid
1.2s	1083×	body	1280	nan
736.0ms	1660×	body	640	valid
625.0ms	882×	body	640	nan
469.0ms	2634×	body	80	overflowed
220.0ms	703×	body	320	valid
203.0ms	477×	body	320	nan
163.0ms	237×	body	640	invalid
153.0ms	115×	body	1280	invalid
145.0ms	1580×	body	80	valid
74.0ms	183×	body	320	invalid
71.0ms	358×	body	160	valid
56.0ms	235×	body	160	nan
31.0ms	516×	body	80	nan
29.0ms	230×	body	80	invalid
18.0ms	76×	body	160	invalid

Details

analyze1.2s

sample193.0ms

simplify59.0ms

prune3.0ms

localize8.0ms

rewrite22.0ms

series56.0ms

simplify82.0ms

prune125.0ms

localize10.0ms

rewrite35.0ms

series98.0ms

simplify81.0ms

prune144.0ms

localize11.0ms

rewrite41.0ms

series64.0ms

simplify54.0ms

prune140.0ms

localize13.0ms

rewrite31.0ms

series83.0ms

simplify63.0ms

prune179.0ms

regimes296.0ms

bsearch2.0ms

simplify3.0ms

end0.0ms

sample6.6s

Profiling